Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn rigid compact complex surfaces and manifolds
174
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
This article investigates the subject of rigid compact complex manifolds. First of all we investigate the different notions of rigidity (local rigidity, global rigidity, infinitesimal rigidity, etale rigidity and strong rigidity) and the relations among them. Only for curves these notions coincide and the only rigid curve is the projective line. For surfaces we prove that a rigid surface which is not minimal of general type is either a Del Pezzo surface of degree >= 5 or an Inoue surface. We give examples of rigid manifolds of dimension n >= 3 and Kodaira dimensions 0, and 2 <=k <= n. Our main theorem is that the Hirzebruch Kummer coverings of exponent n >= 4 branched on a complete quadrangle are infinitesimally rigid. Moreover, we pose a number of questions.
rate research
Read More
For each $n geq 3$ the authors provide an $n$-dimensional rigid compact complex manifold of Kodaira dimension $1$. First they construct a series of singular quotients of products of $(n-1)$ Fermat curves with the Klein quartic, which are rigid. Then using toric geometry a suitable resolution of singularities is constructed and the deformation theories of the singular model and of the resolutions are compared, showing the rigidity of the resolutions.
Using the theory of totally real number fields we construct a new class of compact complex non-K{a}hler manifolds in every even complex dimension and study their analytic and geometric properties.
In this paper, we investigate automorphisms of compact Kahler manifolds with different levels of topological triviality. In particular, we provide several examples of smooth complex projective surfaces X whose groups of $C^infty$-isotopically trivial automorphisms, resp. cohomologically trivial automorphisms, have a number of connected components which can be arbitrarily large.
We prove the unirationality of the Ueno-type manifold $X_{4,6}$. $X_{4,6}$ is the minimal resolution of the quotient of the Cartesian product $E(6)^4$, where $E(6)$ is the equianharmonic elliptic curve, by the diagonal action of a cyclic group of order 6 (having a fixed point on each copy of $E(6)$). We collect also other results, and discuss several related open questions.
In this paper we study Higgs and co-Higgs $G$-bundles on compact Kahler manifolds $X$. Our main results are: (1) If $X$ is Calabi-Yau, and $(E,,theta)$ is a semistable Higgs or co-Higgs $G$-bundle on $X$, then the principal $G$-bundle $E$ is semistable. In particular, there is a deformation retract of ${mathcal M}_H(G)$ onto $mathcal M(G)$, where $mathcal M(G)$ is the moduli space of semistable principal $G$-bundles with vanishing rational Chern classes on $X$, and analogously, ${mathcal M}_H(G)$ is the moduli space of semistable principal Higgs $G$-bundles with vanishing rational Chern classes. (2) Calabi-Yau manifolds are characterized as those compact Kahler manifolds whose tangent bundle is semistable for every Kahler class, and have the following property: if $(E,,theta)$ is a semistable Higgs or co-Higgs vector bundle, then $E$ is semistable.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
